Lie n-derivations of unital algebras with idempotents

Let AA be a unital algebra with nontrivial idempotents. We show that under certain assumptions every Lie n-derivation φ   on AA is of the form φ=d+δ+γφ=d+δ+γ, where d   is a derivation of AA, δ   is both a singular Jordan derivation and an antiderivation of AA, and γ   is a linear map from AA to its center Z(A)Z(A) that vanishes on [⋯[[A,A],A],…,A][⋯[[A,A],A],…,A]. As an application we give a description of Lie n-derivations of unital algebras with wide idempotents.